How to manage the shapekey's position faster?
No, as far as I know, this does not exist in blender without a modification.

Solution: Open all of the shape key filtering options and click the (az) symbol; This will alphabetize your list, and since all of your shapes are so organized in the first place, all you have to do is rename a brand new shape to it's proper category and it should end up there automatically. 



This should put all shape keys under their proper headed, as long as the all the headers are like the ones you show above.